I have 16 circuits that I am trying to attach as a monitoring tool. The object is when I plug this edge connector into a circuit board then the LED will blink on the monitoring tool, stating everything is "ok", if one or two lights stay solid then we have a problem. I choose mosfet's because I need something with high input impedance, to prevent loading that circuit card down. The circuit board sends a signal that is in the microamps and a 3.7 volts logic high. I am looking for a mosfet that can receive a 3.7 Volt logic high through the gate and light a red LED on the drain?

Is there any components that will work better the a mosfet?

 

Digikey shows a lot of NFETs that that turn on with Vgs between 1 and 3V. Start on this page and refine your search from there.

This is an example:

 

About your drawing...the arrow thingy is not the gate. It is internally connected to the source terminal. You can't just declare that you are attaching a wire to it, and not the source terminal.